SOLUTION: Determine whether the graphs of the equations are parallel lines, perpendicular lines, or neither. 3x - 4y = 8 8x + 6y = 8

Algebra ->  Graphs -> SOLUTION: Determine whether the graphs of the equations are parallel lines, perpendicular lines, or neither. 3x - 4y = 8 8x + 6y = 8       Log On


   

Question 237558: Determine whether the graphs of the equations are parallel lines, perpendicular lines, or neither.
3x - 4y = 8
8x + 6y = 8
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

3x-4y=8 Start with the first equation.


-4y=8-3x Subtract 3x from both sides.


-4y=-3x%2B8 Rearrange the terms.


y=%28-3x%2B8%29%2F%28-4%29 Divide both sides by -4 to isolate y.


y=%28%28-3%29%2F%28-4%29%29x%2B%288%29%2F%28-4%29 Break up the fraction.


y=%283%2F4%29x-2 Reduce.


So we can see that the equation y=%283%2F4%29x-2 has a slope m=3%2F4 and a y-intercept b=-2.


8x%2B6y=8 Now move onto the second equation.


6y=8-8x Subtract 8x from both sides.


6y=-8x%2B8 Rearrange the terms.


y=%28-8x%2B8%29%2F%286%29 Divide both sides by 6 to isolate y.


y=%28%28-8%29%2F%286%29%29x%2B%288%29%2F%286%29 Break up the fraction.


y=-%284%2F3%29x%2B4%2F3 Reduce.


So we can see that the equation y=-%284%2F3%29x%2B4%2F3 has a slope m=-4%2F3 and a y-intercept b=4%2F3.


So the slope of the first line is m=3%2F4 and the slope of the second line is m=-4%2F3.


Notice how the slope of the second line m=-4%2F3 is simply the negative reciprocal of the slope of the first line m=3%2F4.


In other words, if you flip the fraction of the second slope and change its sign, you'll get the first slope. So this means that y=%283%2F4%29x-2 and y=-%284%2F3%29x%2B4%2F3 are perpendicular lines. Consequently, this means that 3x-4y=8 and 8x%2B6y=8 are also perpendicular lines.